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arXiv · 2501.12127

On the cohomology of simple Shimura varieties with non quasi-split local groups

Jingren Chi·Thomas J. Haines
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Abstract

We study the Scholze test functions for bad reduction of simple Shimura varieties at a prime where the underlying local group is any inner form of a product of Weil restrictions of general linear groups. Using global methods, we prove that these test functions satisfy a vanishing property of their twisted orbital integrals, and we prove that the pseudostabilization base changes of such functions exist (even though the local group need not be quasi-split) and can be expressed in terms of explicit distributions in the stable Bernstein center. We then deduce applications to the stable trace formula and local Hasse-Weil zeta functions for these Shimura varieties.

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Jingren Chi, Thomas J. Haines. 2025-01-21. On the cohomology of simple Shimura varieties with non quasi-split local groups. https://arxiv.org/abs/2501.12127

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